Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu

doi:10.1214/12-AIHP532

Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu

School of Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.

Original language	English (US)
Pages (from-to)	845-871
Number of pages	27
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	50
Issue number	3
DOIs	https://doi.org/10.1214/12-AIHP532
State	Published - Aug 2014

Keywords

Hawkes processes
Large deviations
Point processes
Rare events
Self-exciting processes

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10.1214/12-AIHP532

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title = "Process-level large deviations for nonlinear Hawkes point processes",

abstract = "In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.",

keywords = "Hawkes processes, Large deviations, Point processes, Rare events, Self-exciting processes",

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KW - Large deviations

KW - Point processes

KW - Rare events

KW - Self-exciting processes

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Process-level large deviations for nonlinear Hawkes point processes

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